On rational homotopy of four-manifolds

2003/09/04 by Svjetlana Terzić, S. Terzic, Terzic, S.
Computer Science · Mathematics · #53C25 #57R17 #57R57 #58A14 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.DG #msc:53C25 #msc:57R17 #msc:57R57 #msc:58A14

paper · pdf · doi:10.48550/arxiv.math/0309076

13 pages, to appear in the Proc. of the Work. Contemporary Geometry and Related Topics (Belgrade, 2002)

arxiv created 2003/09/04 · openalex publication_date 2003/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give explicit formulas for the ranks of the third and fourth homotopy groups of all oriented closed simply-connected four manifolds in terms of their second Betti numbers. We also show that the rational homotopy type of these manifolds is classified by their rank and signature.

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